Scott DePutron Julie Christman Dr. Hasan Dividing Polynomials Lesson Plan Algebra 2 35 Students 2/7/12 80 minutes
Established Goals (Standards): Common Core: A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
A-APR.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) +r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
A-APR.7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
California Math Content 3.0 Students are adept at operations on polynomials, including long division.
Learning Objective: Students will be able to:
Divide polynomials using the methods of long division and synthetic division.
Key Ideas:
Long division
Synthetic division
Essential Questions:
What are the steps used to divide polynomials using long division?
What are the steps used to divide polynomials using synthetic division?
Problems that the students will be doing: 3. (27x4 - 18x2 + 9x) ÷ 9x 4. (x2 + 12x - 160) ÷ (x - 8) 7. (21x2 - 29x - 10) ÷ (3x - 5) 10. (4x3 - 7x + 8) ÷ (2x - 1)
Other ways students might solve these problems:
Students may set up the division vertically and attempt to cancel terms or use the method of long division.
Misconceptions and challenges might students have:
Students may not divide each term in the numerator by the denominator.
Students may cancel out exponents from solely one term in the numerator with one term in the denominator rather than distributing the whole denominator to each term in the numerator.
Students may not distribute the negative sign to the whole binomial when subtracting in long division.
Students may forget to use placeholders for missing terms when using long division.
Students may not remember the steps involved when the remainder is not zero.
Students may not bring down the first term before following to multiply and add when using synthetic division.
Extension Activities:
Dividing Polynomials HW 1
Introduction to synthetic division in following lesson.
Julie Christman
Dr. Hasan
Dividing Polynomials Lesson Plan
Algebra 2
35 Students
2/7/12
80 minutes
Established Goals (Standards):
Common Core:
A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
A-APR.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) +r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
A-APR.7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
California Math Content
3.0 Students are adept at operations on polynomials, including long division.
Learning Objective:
Students will be able to:
Key Ideas:
Essential Questions:
Academic Language:
Key Academic Genres:
Needed Materials:
Lesson Activities:
Assessments:
Problems that the students will be doing:
3. (27x4 - 18x2 + 9x) ÷ 9x
4. (x2 + 12x - 160) ÷ (x - 8)
7. (21x2 - 29x - 10) ÷ (3x - 5)
10. (4x3 - 7x + 8) ÷ (2x - 1)
Other ways students might solve these problems:
Misconceptions and challenges might students have:
Extension Activities: